no hice nada = I did not do anything. English doesn't have double negatives the way Spanish does.

1. "I did not do anything" : Yes, this is fine 2 "I did not do nothing" : This is not a correct translation of "no hice nada". If you say 'I did not do nothing', strictly speaking, this means 'I did something'. Two negative make a positive. That said, many native speakers use this form colloquially. If you go to an English-speaking country, you will hear many less educated people say 'I didn't do nothing'. Don't copy them, and don't use this form yourself. If you, as a non-native, were to use this form, people would presume you were making a mistake. 3. "I did nothing" : This is also fine. It means the same as #1 4. "I did not did anything" and 5. "I did not did nothing": These are simply ungrammatical. The verb form 'I did not did' doesn't exist.

Gracias! Qué tal la tercera?

La segunda como doble negación tendría el sentido de que si hizo algo. La cuarta y quinta están mal. Gramaticalmente non es posible decir eso.